Machine Learning and the Random Walk Puzzle: Forecasting the CAD/USD Exchange Rate with Expanding Window Evaluation and SHAP Interpretability
Organizations: Department of Economics, University of Ottawa, Ottawa, ON K1N 6N5, Canada · Department of Biostatistics and Data Science, Celia Scott Weatherhead School of Public Health and Tropical Medicine at Tulane University, New Orleans, LA 70112, USA · School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, Edinburg, Texas, USA · Department of Statistics, Western Michigan University, Kalamazoo, Michigan, USA · Department of Economics, Western Michigan University, Kalamazoo, Michigan, USA · Robinson College of Business, Georgia State University, Atlanta, USA. · Department of Mathematics & Statistics, University of North Florida, Jacksonville, Florida, USA. · Department of Epidemiology and Biostatistics, University of Arizona, USA · Department of Statistics and Actuarial Science, University of Ghana, Accra, Ghana
Abstract
This study examines whether machine learning (ML) models can outperform the naive random walk benchmark in forecasting the monthly USD/CAD exchange rate. Using daily data from the Bank of Canada spanning January 2017 to May 2026, resampled into 113 monthly observations, five ML models are evaluated: linear regression, random forest, gradient boosting, XGBoost, and AdaBoost. These models are benchmarked against the naive random walk model and exponential smoothing with Holt-Winters seasonality (ETS). All models are evaluated using an expanding-window framework to maintain strict out-of-sample integrity, and forecast-accuracy differences are assessed using the Diebold-Mariano (DM) test. Structural break detection identifies four significant breakpoints in the series, corresponding to the escalation of the US-China trade war in 2018, the COVID-19 economic recovery in 2020, the peak of the Bank of Canada rate-hiking cycle in 2022, and the start of the Bank of Canada rate-cutting cycle in 2024. SHAP, or Shapley Additive Explanations, analysis is applied to interpret the drivers of the best-performing ML model. The results show that the naive random walk model remains a formidable benchmark. Linear regression is the only model that statistically outperforms the naive random walk model, with a DM statistic of 3.0585 and a p value of 0.0071, whereas the ML ensemble models show only marginal differences. Random Forest with an expanding-window framework achieves the lowest MAPE of 1.17 percent among all models except the random walk. SHAP analysis confirms that short-term lags, particularly lag1 and lag2, and recent rolling means dominate predictions, consistent with the near-random-walk behavior of exchange rates.